# Father and son turn years

In 1999, a father and son celebrating their birthday on the same day, used two number-shaped candles to represent their age. Both use the same two candles, only that they invert the order of placing them on the cake to indicate their age. Interestingly, the age of the father coincides with the last two figures of the year of birth of the son and the age of the son coincides with the last two figures of the year of birth of the father. Knowing that the difference between them is 27 years,

How old is each one?

#### Solution

Although it is possible to solve it through a system of equations with two unknowns, there is another way to get the answer.

Let's call AB at the age of the father where each letter represents a digit. Therefore, the child's age is BA.
The year of birth of the son will be 19AB and that of father 19BA.

Then it is fulfilled that: 19AB + BA = 1999

Therefore we know that A + B = 9. For this, the following possibilities are given:

 Father's age Son's age 90 09 81 18 72 27 63 36 54 45

Then we see that the only ones that fulfill the property of differentiating in 27 years are those corresponding to 63 years for the father and 36 years for the son.